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Daily Wind Patterns: Understanding of ProcessesRoel Vining and Dr. James Gregory

Introduction

Wind is an important variable for several processes, including wind erosion andevapotranspiration estimation. Vining and Allen (1993) describe the need to consider a range of

air resource related variables, including wind, in integrated resource management planning.

Therefore, it is desirable that the patterns of wind speed changes over a day be investigated and

described. Like most climatic variables, wind tends to be both random and cyclic as time varies.

Sine waves have often been used to describe average diurnal wind speed variations. Work by

Gregory, et al. (1994) indicates that wind speed at Lubbock, TX is near constant during dark

hours, and follows a curvilinear pattern during daylight hours. Later work by Gregory, et al.

(1996) shows that diurnal wind patterns at five locations in the Great Plains follow a pattern

similar to that observed at Lubbock, TX.

The intent of this investigation is to examine diurnal wind speed patterns for various sites indifferent climates across the United States, applying the previously developed model to see

whether it holds over a wider geographic range.

The model used to generate wind speed data to compare to the measured data is described in

detail by Gregory, et al. (1994). It takes the form of:

ZD = A1-A4(H-A3)2

(1)

If ZD > 0, then ZD = 0 (2)

WS = A2+ZD (3)

Where WS = predicted wind speed

H = hour of day

A1 = the amplitude of the daytime wave

A2 = the wind speed at night

A3 = the time of day that maximum wind occurs, and

A4is inversely related to length of daylight hours squared and directly related to A2.

The strength of the model is its ability to predict strong downmixing of momentum from upper

level winds to the surface as nighttime inversions break from solar heating. A1represents thepotential of strength for downmixing by controlling the increase in wind speed from daybreak to

time of maximum wind speed. One reason for selecting climate stations in various locations

around the country was to examine the changes in potential downmixing depending on location,

and how those changes would potentially affect the models ability to predict diurnal wind speed.

We must also account for variations away from mean wind speed values. Gregory (1989)

developed an equation to predict probability of wind speed variations away from mean daily

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values assuming a constant standard deviation over all months of data for a site. Probability is

given by:

Pc = 100(1-e-K1(1-e-K2SK3)SK3) (4)

Where Pc = Cumulative probability

S = Speed ratio (magnitude of speed of interest over mean speed for a given

day), and

K1,2,3 = coefficient values

The standard deviation of the wind data is proportional to the magnitude of the average wind

speed for the time duration being considered. The coefficient of variation is approximately

constant from month to month. This relationship causes the probability distribution for a given

time period to be the same as other time periods when the wind speed is compared to the mean

value for the given time period. Therefore, we should be able to scale the scatter of wind speed

for hourly as well as monthly average wind speed.

Hourly wind values averaged over each month were calculate for data from 10 sites across the

United States: Spokane, WA, Phoenix, AZ, Fresno, CA, Salt Lake City, UT, Casper, WY,

Bismarck, ND, Des Moines, IA, Baton Rouge, LA, Albany, NY, and Atlanta, GA. The data are

from the climate database of the Natural Resources Conservation Service Water and Climate

Center. The period of record for all stations was from 1982 to 1990. These locations were

chosen for a number of reasons: geographic distribution, local topographic variations (for

example, mountainous west versus plains-cornbelt), site elevation, local climate, and data

availability. While these sites represent only a limited cross-section of locations across the

country, analysis of these data should provide some insight into the characteristics of diurnal wind

speed patterns in diverse climate regimes.

Discussion of Hourly Analysis

Results of the hourly analysis of wind speed are shown for January and July in Table 1. An

example plot of the average and predicted data for Bismarck, ND is shown in figure 1. At most

locations, the developed model appears to accurately describe the average diurnal variations of

wind speed. Albany, Atlanta, and Des Moines had R2 values above 0.90 for both months

analyzed. Earlier research hypothesized that high accuracy from the model could be expected in

the Great Plains, where wind speeds for much of the year are influenced by downmixing from the

jet stream. Surprisingly, data for Atlanta, Baton Rouge, and Albany also showed good

correlation between measured and estimated values. Atlanta and Baton Rouge have elevationsnear sea level and experience high relative humidity. Both factors should dampen the downmixing

process. Also, these locations are generally not under the main jet stream core during January or

July; however, their predictable wind patterns imply that more than location under a jet stream

core, thickness of the overlying atmosphere, or relative humidity will influence diurnal wind

patterns.

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Table 1: Hourly wind speed analysis correlation coefficients (R2) for January and July

January

Location R 2

Albany 0.96Atlanta 0.93

Baton Rouge 0.94

Bismarck 0.89

Casper 0.89

Des Moines 0.90

Fresno 0.67

Phoenix 0.88

Salt Lake City 0.69

Spokane 0.87

July

Location R 2

Albany 0.96Atlanta 0.94

Baton Rouge 0.82

Bismarck 0.96

Casper 0.97

Des Moines 0.95

Fresno 0.51

Phoenix 0.77

Salt Lake City 0.87

Spokane 0.88

Diurnal wind patterns at locations near to strong orographic influences did not follow thepatterns predicted by the model. In particular, wind at Fresno in July followed a pattern of

increasing speed during daylight hours and decreasing speed during nighttime hours. The

other locations with the potential for orographic influence (Phoenix and Salt Lake City)

showed R2values lower than the Great Plains locations, but the measured wind patterns

generally followed the model predictions. Casper has high winds due to mountain gaps

upwind; however, Casper also displays a strong downmixing pattern.

The conclusion is that the model appears to function effectively for data from January and

July with only a few exceptions. The comparisons for January at all locations compare

favorably with those from July. Thus, the functions that drive diurnal wind speed patterns,

whether they be synoptic or local in scale, appear to function similarly without regard to

time of year, at least in January and July. It is also obvious that average diurnal wind

speed patterns are cyclic by do not follow a sine wave. Finally, the processes that cause

these wind patterns may have a universal nature. Recent measurements of wind on Mars

have provided data with a similar pattern (personal communication with Dr. Gregory

Wilson, Arizona State University, 1997).

Discussion of Probability Distributions

Results of the probability analysis for Baton Rouge are shown in Figure 2. These resultsare for both 1:00 a.m. and 2:00 p.m. local time. Note that neither day nor night variations

nor monthly variations caused the probability functions to fail. These relationships hold

for the analyses at each of the locations. Based on the relationship between the standard

deviation of the wind speed and the wind speed, we can assume that variations in the

probability of a specified wind speed could be explained by a single probability function

using the ratio of the specified speed to the average speed. These analyses bring the

conclusion that one probability function does explain variations in the wind speed ratio.

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This result is fortunate because it enables one to model wind speed variations with a

relatively simple model. This model, however, should not be used to model extreme

winds for design purposes since extreme winds are only a small fraction of all winds and

tend to be caused by extreme weather conditions.

Figure 1: Average (checkered line) and predicted values of hourly wind speed for

Bismarck, ND for January data.

0

2

4

6

8

10

12

1 3 5 7 911

13

15

17

19

21

23

WindSpeed(knots)

Bismarck R2=0.89

Figure 2: Average (checkered line) and predicted values of hourly wind speed for

Fresno, CA for July data.

0

1

2

3

4

5

6

7

8

9

10

1 3 5 7 911

13

15

17

19

21

23

WindSpeed(knots)

Fresno R2

=0.51

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Figure 3: Cumulative probability plots for Baton Rouge.

Baton Rouge 1:00 am

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15

Speed Ratio

CumulativeProbability

Baton Rouge 2:00 pm

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15

SpeedRatio

CumulativeProbabilit

Limitations

It is important to recognize that the data (both measured and modeled) represent long

term averages (9 years, from 1982 to 1990, in all cases). Clearly, the relationships

described by the equations would not hold well if we were dealing with data for a specific

day. Cloud cover, synoptic conditions, frontal passage, and local effects will influence

instantaneous wind speed more than long term conditions. The results do show, though,

that at locations where local orographic features are not in a position to influence local

climate, the model accurately predicts average wind speeds. We conclude that the simple

equations used in this analysis can be adequate predictors of monthly average wind speeds

in many regions of the continental United States. These equations could be used in a

variety of models to simulate average wind speed. This model should prove effective in

estimating wind speed for use in wind erosion, evapotranspiration, and pollution

dispersion models. At locations where local geographic features affect wind speed, more

specific predictive equations will need to be developed to address those concerns affected

by locality.

Finally, no attempt was made at this time to relate coefficients in the equations to other

variables, such as elevation, relative humidity, influence of jet stream location, etc. Values

for A1, A2, A3, and A4 were successfully related to a yearly cycle by Gregory, et al.

(1996) for Great Plains sites. More research is needed to develop these relationships for

the whole of the United States. This research could have value in relating climate change

to global temperature changes and anticipated shifts in jet stream patterns.

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References

Gregory, J.M. 1989. Wind data generation for Great Plains locations. American Society

of Agricultural Engineers, New Orleans, LA.

Gregory, J.M., R.E. Peterson, J.A. Lee, and G.R. Wilson. 1994. Modeling wind andrelative humidity effects on air quality. International Specialty Conference on Aerosols

and Atmospheric Optics: Radiative Balance and Visual Air Quality. Sponsored by Air and

Waste Management Association and American Geophysical Union, Snowbird, Utah.

Gregory, J.M., G.R. Wilson, and R.C. Vining. 1996. Modeling hourly and daily wind and

relative humidity. International Conference on Air Pollution from Agricultural Operations.

Midwest Plan Service, Ames, IA, p 183-190.

Vining, R.C. and M. Allen. 1993. Consideration of the air resource through total resource

management. IN Integrated Resource Management and Landscape Modification for

Environmental Protection. Proceedings of the International Symposium, Chicago, IL.American Society of Agricultural Engineers, St. Joseph, MI, p 20-28.

Wilson, G.R. 1997. Personal Communication.